Peter Woit reports the claim that the "
abc conjecture" has been proven:
http://www.math.columbia.edu/~woit/wordpress/?p=5104
The abc conjecture is a number theory conjecture from 1985 which has
been called "the most important unsolved problem in
Diophantine analysis."
Peter links to this more detailed report and discussion of the claim:
http://quomodocumque.wordpress.com/2012/09/03/mochizuki-on-abc/
and here's a more layman-friendly interpretation of it from a few years back:
http://bit-player.org/2007/easy-as-abc
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